A mixed graph is a graph with undirected and directed edges. Guo and Mohar in 2017 determined all mixed graphs whose Hermitian spectral radii are less than 2. In this paper, we give a sufficient condition which can make Hermitian spectral radius of a connected mixed graph strictly decreasing when an edge or a vertex is deleted, and characterize all mixed graphs with Hermitian spectral radii at most 2 and with no cycle of length 4 in their underlying graphs.

中文翻译：

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在混合图上，厄米光谱半径最大为2

混合图是具有无向和有向边的图。Guo和Mohar在2017年确定了Hermitian谱半径小于2的所有混合图。在本文中，我们给出了充分的条件，可以使连接的混合图的Hermitian谱半径在删除边或顶点时严格减小，并且表征所有混合图，且其埃尔米特谱半径至多为2，并且其基础图中的长度为4。